Is this older man into me? What do I do?

Signs he isn't (?): -I had to charge my phone in his hotel room briefly and he at first said 'this is inappropriate.'-He never physically made a move enough to kiss me -We go through hot and cold phases when we run into each other, usually avoid each other to make the other seem like we hate each other. He's asked friends of mine why I hate him and I the same.

Signs he is (?):-I catch him staring at me across the room at events-On the night, he kept his hands on my thigh as we had a long talk about some things-In the nightclub with the group, he kept his hand on my lower back-In his hotel room, he got so close multiple times that my nose was touching his cheek-He kept referencing either my looks or that he wants me by only saying "you know!"

Is there maybe a chance here for something? If so, what's the next move?

The way you're describing makes him sound quite a bit older. An older guy hitting on a younger mostly means he just wants sex. He's past any faze of finding that special someone and having a happily ever after. I'd say keep your distance.